# Syllabus for Master of Science (Statistics) Academic Year  (2021)

 1 Semester - 2021 - Batch Course Code Course Type Hours Per Week Credits Marks MST131 PROBABILITY THEORY Core Courses 5 5 100 MST132 DISTRIBUTION THEORY Core Courses 5 5 100 MST133 MATRIX THEORY AND LINEAR MODELS Core Courses 5 5 100 MST134 RESEARCH METHODOLOGY AND LATEX Core Courses 2 2 50 MST171 SAMPLE SURVEY DESIGNS Core Courses 6 5 150 MST172 STATISTICAL COMPUTING USING R Core Courses 5 4 150 2 Semester - 2021 - Batch Course Code Course Type Hours Per Week Credits Marks MST231 STATISTICAL INFERENCE-I Core Courses 4 4 100 MST232 STOCHASTIC PROCESSES Core Courses 4 4 100 MST233 CATEGORICAL DATA ANALYSIS Core Courses 4 4 100 MST271 REGRESSION ANALYSIS Core Courses 6 5 150 MST272 STATISTICAL COMPUTING USING PYTHON Core Courses 5 4 150 MST273A PRINCIPLES OF DATA SCIENCE AND DATA BASE TECHNIQUES Discipline Specific Elective Courses 5 4 150 MST273B SURVIVAL ANALYSIS Discipline Specific Elective Courses 5 4 150 MST273C OPTIMIZATION TECHNIQUES Discipline Specific Elective Courses 5 4 100 MST281 RESEARCH PROBLEM IDENTIFICATION AND FORMULATION Core Courses 2 1 50 3 Semester - 2020 - Batch Course Code Course Type Hours Per Week Credits Marks MST331 STATISTICAL INFERENCE II Core Courses 4 4 100 MST332 MULTIVARIATE ANALYSIS Core Courses 4 4 100 MST371 TIME SERIES ANALYSIS Core Courses 6 5 150 MST372A STATISTICAL MACHINE LEARNING Discipline Specific Elective Courses 5 4 150 MST372B BIOSTATISTICS Discipline Specific Elective Courses 5 4 150 MST372C RELIABILITY ENGINEERING Discipline Specific Elective Courses 5 4 150 MST373A NUMERICAL ANALYSIS Discipline Specific Elective Courses 5 4 150 MST373B NON-PARAMETRIC METHODS Discipline Specific Elective Courses 5 4 150 MST373C THEORY OF GAMES AND STATISTICAL DECISIONS Discipline Specific Elective Courses 5 4 150 MST381 RESEARCH MODELING AND IMPLEMENTATION Core Courses 8 4 200 4 Semester - 2020 - Batch Course Code Course Type Hours Per Week Credits Marks MST431 ADVANCED OPERATIONS RESEARCH Core Courses 4 4 100 MST432 DESIGN AND ANALYSIS OF EXPERIMENTS Core Courses 4 4 100 MST433 STATISTICAL QUALITY CONTROL Core Courses 4 4 100 MST471A NEURAL NETWORKS AND DEEP LEARNING Discipline Specific Elective Courses 5 4 150 MST471B SPATIAL STATISTICS Discipline Specific Elective Courses 5 4 150 MST471C BIG DATA ANALYTICS Discipline Specific Elective Courses 5 4 150 MST472A HIGH DIMENSIONAL STATISTICAL ANALYSIS Discipline Specific Elective Courses 5 4 150 MST472B STATISTICAL GENETICS Discipline Specific Elective Courses 5 4 150 MST472C ACTUARIAL METHODS Discipline Specific Elective Courses 5 4 150 MST473A BAYESIAN STATISTICS Discipline Specific Elective Courses 5 4 150 MST473B CLINICAL TRIALS Discipline Specific Elective Courses 5 4 150 MST473C RISK MODELING Discipline Specific Elective Courses 5 4 150 MST481 SEMINAR PRESENTATION Skill Enhancement Courses 2 1 50

 Introduction to Program: Master of Science in Statistics at CHRIST (Deemed to be University) offers the students an amalgam of knowledge on theoretical and applied statistics on a broader spectrum. Further, it intends to impart awareness of the importance of the conceptual framework of statistics across diversified fields and provide practical training on statistical methods for carrying out data analysis using sophisticated programming languages and statistical softwares such as R, Python, SPSS, EXCEL, etc. The course curriculum has been designed in such a way to cater for the needs of stakeholders to get placements in industries and institutions on successful completion of the course and to provide those ample skills and opportunities to meet the challenges at the national level competitive examinations like CSIR NET in Mathematical Science, SET, Indian Statistical Service (ISS) etc. Programme Outcome/Programme Learning Goals/Programme Learning Outcome:PO1: Engage in continuous reflective learning in the context of technology and scientific advancement.PO2: Identify the need and scope of Interdisciplinary research.PO3: Enhance research culture and uphold scientific integrity and objectivityPO4: Understand the professional, ethical and social responsibilitiesPO5: Understand the importance and the judicious use of technology for the sustainability of the environmentPO6: Enhance disciplinary competency, employability and leadership skillsProgramme Specific Outcome:PSO1: Demonstrate analytical and problem-solving skills to identify and apply appropriate principles and methodologies of statistics in real-time problems.PSO2: Demonstrate the execution of statistical experiments or investigations, analyse and interpret using appropriate statistical methods, including statistical software and report the findings of experiments or studies accurately.PSO3: Demonstrate acquaintance with contemporary trends in industrial/research settings and innovate novel solutions to existing problems.PSO4: Demonstrate competency as a statistician in order to succeed in a broad range of analytic, scientific, government, financial, health, technical and other fields Assesment Pattern CIA - 50% ESE - 50% Examination And Assesments CIA - 50% ESE - 50%
 MST131 - PROBABILITY THEORY (2021 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:100 Credits:5 Course Objectives/Course Description Probability is a measure of uncertainty and forms the foundation of statistical methods. This course makes students use measure-theoretic and analytical techniques for understanding probability concepts. Course Outcome CO1: Relate measure and probability conceptsCO2: Analyse probability concepts using the measure-theoretic approachCO3: Evaluate conditional distributions and conditional expectationsCO4: Make use of limit theorems in the convergence of random variables
Unit-1
Teaching Hours:15
Probability and Random variable

Sets – functions - Sigma field – Measurable space – Sample space – Measure – Probability as a measure - Inverse function - Measurable functions – Random variable - Induced probability space - Distribution function of a random variable: definition and properties.

Unit-2
Teaching Hours:15
Expectation and Generating functions

Expectation and moments: Definition and properties – Probability generating function - Moment generating functions - Moment inequalities: Markov’s, Chebychev’s, Holder, Jenson and basic inequalities - Characteristic function and properties (idea and statement only).

Text Books And Reference Books:
1. Rohatgi, V.K. and Salah, A.K.E, (2015), An Introduction to Probability and Statistics, 3rd Ed., John Wiley & Sons.
2. Bhat, B.R, (2014), Modern Probability Theory, 4th Ed., New Age International.
1. Feller W, (2008), An Introduction to Probability Theory and its Applications, Volume I , 3rd Ed., Wiley Eastern.
2. Feller W, (2008), An Introduction to Probability Theory and its Applications, Volume II,3rd Ed.,  Wiley Eastern.
3. Billingsley, P. (2008). Probability and measure. John Wiley & Sons.
4. Basu A.K, (2012), Measure Theory and Probability, 2nd Ed., PHI.
5. Durrett R, (2010), Probability: Theory and Examples. 4th ed. Cambridge University Press, 2010.
Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST132 - DISTRIBUTION THEORY (2021 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:5
Max Marks:100
Credits:5

Course Objectives/Course Description

Probability distributions are used in many real-life phenomena. This course makes students understand different probability distributions and model real-life problems using them.

Course Outcome

CO1: Classify different families of probability distributions.

CO2: Analyse well-known probability distributions as a special case of different families of distribution

CO3: Identify different distributions arising from sampling from the normal distribution.

CO4: Apply probability distribution in various statistical problems.

Unit-1
Teaching Hours:15
Discrete Distributions

Modified power series family and properties - Binomial - Negative binomial, Logarithmic series and Lagrangian distributions and their properties as special cases of the results from modified power series family - hypergeometric distribution and its properties.

Unit-2
Teaching Hours:15
Continuous Distributions

Pearsonian system of distributions - Beta, Gamma, Pareto and Normal as special cases of the Pearson family and their properties - Exponential family of distributions.

Text Books And Reference Books:
1. Rohatgi, V.K. and Salah, A.K.E. (2015) An Introduction to Probability and Statistics, 3rd Ed., John Wiley & Sons.
2. Krishnamoorthy, K. (2016). Handbook of statistical distributions with applications. CRC Press.
1. Johnson N.L, Kotz S and Kemp A.W (2005) Univariate discrete distributions, 3rd Ed., John Wiley.
2.  Johnson N.L, Kotz S and Balakrishnan N (2017) Continuous univariate distributions I & II, John Wiley.
3.  Johnson N.L, Kotz S and Balakrishnan N (2000) Multivariate Distribution, 2nd Ed., John Wiley.
4. Arnold B.C, Balakrishnan N and Nagaraja H.N (2012) A first course in order statistics.
5. Elderton, W. P., & Johnson, N. L. (2009). Systems of frequency curves, Cambridge University press.
Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST133 - MATRIX THEORY AND LINEAR MODELS (2021 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:5
Max Marks:100
Credits:5

Course Objectives/Course Description

This course is offered to make students understand the critical aspects of matrix theory and linear models used in different areas of statistics such as regression analysis, multivariate analysis, design of experiments and stochastic processes.

Course Outcome

CO1: Demonstrate the understanding of vector-space and different operations on it

CO2: Analyse system of linear equations using matrix theoretic approach

CO3: Identify applications of matrix theory in statistical problems

CO4: Apply matrix theory in linear models

Unit-1
Teaching Hours:15
System of linear equations

Matrix operations - Linear equations - row reduced and echelon form -  Homogenous system of equations -  Linear dependence

Unit-2
Teaching Hours:15
Vector Space

Vectors - Operations on vector space - subspace - nullspace and column space - Linearly independent sets - spanning set - bases - dimension - rank - change of basis.

Text Books And Reference Books:
1. David C. Lay, Steven R. Lay, Judi J. McDonald (2016) Linear algebra and its applications. Pearson.
2. Lipschutz, S., & Lipson, M. L. (2018). Schaum's Outline of Linear Algebra. McGraw-Hill Education.
1. Searle, S. R., & Khuri, A. I. (2017). Matrix algebra useful for statistics. John Wiley & Sons.
2. Rencher, A. C., & Schaalje, G. B. (2008). Linear models in statistics. John Wiley & Sons.
3. Khuri, A. I. (2003). Advanced calculus with applications in statistics. Hoboken, NJ: Wiley-Interscience.
4. Gentle, J. E. (2017) Matrix algebra- Theory, Computations and Applications in Statistics. Springer texts in statistics, Springer, New York.
5. Strang, G. (2006) Linear Algebra and its Applications: Thomson Brooks. Cole, Belmont, CA, USA.
Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST134 - RESEARCH METHODOLOGY AND LATEX (2021 Batch)

Total Teaching Hours for Semester:30
No of Lecture Hours/Week:2
Max Marks:50
Credits:2

Course Objectives/Course Description

To acquaint students with different methodologies in statistical research and to make them prepare scientific articles using LaTeX.

Course Outcome

CO1: Define a research problem

CO2: Identify a suitable methodology for solving the research problem

CO3: Create scientific articles using LaTeX.

 Unit-1 Teaching Hours:15 Fundamentals of research Objectives - Motivation - Utility - Concept of theory - empiricism - deductive and inductive theory - Characteristics of the scientific method - Understanding the language of research - Concept - Construct - Definition - Variable - Research Process  Problem Identification & Formulation - Research Question – Investigation Question - Logic & Importance Unit-2 Teaching Hours:15 Scientific writing Principles of mathematical writing - LaTeX: installing packages and editor, preparing title page - mathematical expressions - tables - importing graphics - bibliography - writing a research paper - survey article - thesis writing - Beamer: preparing presentations Text Books And Reference Books: Kothari, C. R. and Garg, G. (2014). Research methodology: Methods and techniques. 3rd Ed., New Age International. L. Lamport (2014), LaTeX, a Document Preparation System, 2nd ed, Addison-Wesley. Essential Reading / Recommended Reading1.Grätzer, G. (2013). Math into LATEX. Springer Science & Business Media. Evaluation PatternCIA - 50% ESE - 50% MST171 - SAMPLE SURVEY DESIGNS (2021 Batch) Total Teaching Hours for Semester:90 No of Lecture Hours/Week:6 Max Marks:150 Credits:5 Course Objectives/Course Description This course aims to impart the concepts of survey sampling theory and the analysis of complex surveys, including methods of sample selection, estimation, sampling variance, standard error of estimation in a finite population, development of sampling theory for use in sample survey problems and sources of errors in surveys. Course Outcome CO1: List different steps in designing a sample survey.CO2: Analyse different sample survey designs and find estimators. CO3: Identify the use of different sample survey designs.CO4: Apply suitable sample survey design in real-life problems.
 Unit-1 Teaching Hours:18 Random sampling designs Sampling vs census, simple random sampling: with (SRS) and without replacement (SRSWOR) of units, estimators of mean, total and variance, determination of sample size, sampling for proportions, Stratified sampling scheme: estimation and allocation of sample size, comparison with simple random sampling schemes.  Lab Exercises: 1. Drawing samples with SRSWR and SRSWOR and estimation of parameters 2. Estimation of parameters using a sample of proportions 3. Drawing stratified sample and estimation of parameters Unit-2 Teaching Hours:18 Ratio and regression estimators Bias and mean square error, estimation of variance, confidence interval, comparison with mean per unit estimator, optimum property of ratio estimator, unbiased ratio type estimator, ratio estimator in stratified random sampling, Difference estimator and Regression estimator:- Difference estimator, regression estimator, comparison of regression estimator with mean per unit and ratio estimator, regression estimator in stratified random sampling. Lab Exercises: 4. Estimation using ratio estimator 5. Estimation using regression estimator 6. Ratio estimator and regression estimator in stratified sampling Text Books And Reference Books:1. Arnab, R. (2017). Survey sampling: Theory and Applications. Academic Press. 2. Singh, D. and Chaudharay, F.S. (2018) Theory and Analysis of Sample Survey Designs, New Age International. Essential Reading / Recommended Reading1. Cochran, W.G. (2007) Sampling Techniques, Third edition, John Wiley & Sons. 2. Singh, S. (2003). Advanced Sampling: Theory and Practice. Kluwer. 3. Des Raj and Chandhok, P. (2013) Sampling Theory, McGraw Hill.  4. Mukhopadhay, P (2009) Theory and methods of survey sampling, Second edition, PHI Learning Pvt Ltd., New Delhi. 5. Sampath, S. (2005) Sampling theory and methods, Alpha Science International Ltd., India. 6. Lumley, T. (2011). Complex surveys: a guide to analysis using R. John Wiley & Sons. Evaluation PatternCIA - 50% ESE - 50% MST172 - STATISTICAL COMPUTING USING R (2021 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description The programming skill in R helps students to perform statistical computations with ease. This course equips students with knowledge of R programming to develop statistical models for real-world problems Course Outcome CO1: Demonstrate the understanding of basic concepts of R programmingCO2: Build useful programs with functionsCO3: Analyse various data using R.CO4: Create visualisation of data using RCO5: Compare different methods of simulating random numbers
 Unit-1 Teaching Hours:15 Introduction R and R studio - Variables - Functions - Vectors - Expressions and assignments - Logical expressions - Matrices - The workspace - R markdown. Practical Assignments: 1. Demonstrate variables and functions in R 2. Creating vectors and matrices and associated operations in R 3. Logical and arithmetic operations in R Unit-2 Teaching Hours:15 Basic Programming Loops: if, for, while - Program flow - Basic debugging  - Good programming habits -  Input and outputs: Input from a file and output to a file  Practical Assignments: 4. Illustration of control structures: if, else, for 5. Illustration of control structures: while, repeat, break, next and ifelse Text Books And Reference Books:1.Jones, O., Maillardet. R. and Robinson, A. (2014). Introduction to Scientific Programming and Simulation Using R. Chapman & Hall/CRC, The R Series. 2.Matloff, N. (2016). The art of R programming: A tour of statistical software design. No Starch Press. Essential Reading / Recommended Reading1.Crawley, M, J. (2012). The R Book, 2nd Edition. John Wiley & Sons. 2.Chambers, J. M. (2008). Software for Data Analysis-Programming with R. Springer-Verlag, New York. Evaluation PatternCIA - 50% ESE - 50% MST231 - STATISTICAL INFERENCE-I (2021 Batch) Total Teaching Hours for Semester:60 No of Lecture Hours/Week:4 Max Marks:100 Credits:4 Course Objectives/Course Description To provide a strong mathematical and conceptual foundation in the methods of parametric estimation and their properties. Course Outcome CO1: List properties of estimators.CO2: Identify a suitable estimation method.CO3: Analyse likelihood function and apply different root solving methods to find estimatorsCO4: Construct confidence intervals for parameters involved in the model.
Unit-1
Teaching Hours:12
Sufficiency

Sufficiency - factorisation theorem - minimal sufficiency - exponential family and completeness - Ancillary statistics and Basu's theorem

Unit-2
Teaching Hours:12
Unbiasedness

UMVUE - Fisher Information and Cramer-Rao inequality - Chapman-Robbin’s and Bhattacharya bounds - Rao-Blackwell theorem - Lehman-Scheffe theorem - Unbiased estimation

Text Books And Reference Books:
1.  Kale, B. K. and Muralidharan, K.(2015). Parametric Inference: An Introduction. Alpha Science Int. Ltd.
2. Srivastava, A. K., Khan, A. H. and Srivastava, N. (2014). Statistical Inference: Theory of Estimation. PHI Learning Pvt. Ltd, New Delhi.

1.Casella, G., & Berger, R. L. (2002). Statistical inference. Pacific Grove, CA: Duxbury.

2.Silvey, S. D. (2017). Statistical inference. Routledge.

3.Trosset, M. W. (2009). An introduction to statistical inference and its applications with R. Chapman and Hall/CRC.

4.Dixit, U. J. (2016). Examples in parametric inference with R, Springer.

5.Lehmann, E. L., & Casella, G. (2006). Theory of point estimation, 2nd Ed. Springer.

6.Robert, C., & Casella, G. (2013). Monte Carlo statistical methods. Springer

Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST232 - STOCHASTIC PROCESSES (2021 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:4
Max Marks:100
Credits:4

Course Objectives/Course Description

To equip the students with theoretical and practical knowledge of stochastic models which are used in economics, life sciences, engineering etc.

Course Outcome

CO1: List different stochastic models.

CO2: Identify ergodic Markov chains.

CO3: Analyse queuing models using continuous-time Markov chains

CO4: Apply Brownian motion in finance problems.

Unit-1
Teaching Hours:12
Introduction

A sequence of random variables - definition and classification of the stochastic process - autoregressive processes and Strict Sense and Wide Sense stationary processes.

Unit-2
Teaching Hours:12
Discrete time Markov chains

Markov Chains: Definition, Examples - Transition probability matrix -  Chapman-Kolmogorv equation - classification of states - limiting and stationary distributions - ergodicity - discrete renewal equation and basic limit theorem - Absorption probabilities - Criteria for recurrence - Generic application: hidden Markov models.

Text Books And Reference Books:

1.Karlin, S. and Taylor, H.M. (2014). A first course in stochastic processes. Academic Press.

2.S. M. Ross (2014). Introduction to Probability Models. Elsevier.

1.Feller, W. (2008) An Introduction to Probability Theory and its Applications, Volume I&II, 3rd Ed., Wiley Eastern.

2.J. Medhi (2009) Stochastic Processes, 3rd Edition, New Age International.

3.Dobrow, R.P. (2016), Introduction to Stochastic Processes with R, Wiley Eastern.

4.Cinlar, E. (2013). Introduction to stochastic processes. Courier Corporation.

Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST233 - CATEGORICAL DATA ANALYSIS (2021 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:4
Max Marks:100
Credits:4

Course Objectives/Course Description

Categorical data analysis deals with the study of information captured through expressions or verbal forms. This course equips the students with the theory and methods to analyse and categorical responses.

Course Outcome

CO1: Describe the categorical response.

CO2: Identify tests for contingency tables.

CO3: Apply regression models for categorical response variables.

CO4: Analyse contingency tables using log-linear models.

Unit-1
Teaching Hours:12
Introduction

Categorical response data - Probability distributions for categorical data - Statistical inference for discrete data

Unit-2
Teaching Hours:12
Contingency tables

Probability structure for contingency tables - Comparing proportions with 2x2 tables - The odds ratio - relative risk - Tests for independence - Association of IXJ tables

Text Books And Reference Books:

1.       Agresti, A. (2012). Categorical Data Analysis, 3rd Edition. New York: Wiley

2.       Agresti, A. (2010). Analysis of ordinal categorical data. John Wiley & Sons.

1.      Le, C.T. (2009). Applied Categorical Data Analysis and Translational Research, 2nd Ed., John Wiley and Sons.

2.      Stokes, M. E., Davis, C. S., & Koch, G. G. (2012). Categorical data analysis using SAS. SAS Institute.

3.      Agresti, A. (2018). An introduction to categorical data analysis. John Wiley & Sons.

4.      Bilder, C. R., & Loughin, T. M. (2014). Analysis of categorical data with R. Chapman and Hall/CRC.

Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST271 - REGRESSION ANALYSIS (2021 Batch)

Total Teaching Hours for Semester:90
No of Lecture Hours/Week:6
Max Marks:150
Credits:5

Course Objectives/Course Description

Regression models are mainly used in establishing a relationship among variables and predicting future values. It got applications in various domain such as finance, life science, management, psychology, etc. This course is designed to impart the knowledge of statistical model building using regression technique.

Course Outcome

CO1: Formulate simple and multiple regression models

CO2: Identify the correct regression model for the given problem

CO3: Apply non-linear regression in real-life problems

CO4: Analyse the robustness of the regression model.

 Unit-1 Teaching Hours:18 Linear regression model Linear Regression Model: Simple and multiple -  Least squares estimation -  Properties of the estimators - Maximum likelihood estimation -  Estimation with linear restrictions -  Hypothesis testing -  confidence intervals. Practical Assignments: 1.     Build a simple linear model and interpret the data. 2.     Construct confidence interval for the simple linear model 3.     Build a multiple linear models and estimate its parameters. 4.     Construct confidence interval for multiple linear model Unit-2 Teaching Hours:18 Model adequacy Residual analysis -  Departures from underlying assumptions -  Effect of outliers - Collinearity - Nonconstant variance and serial correlation -  Departures from normality -  Diagnostics and remedies.  Practical Assignments: 5.     Carry out residual analysis and validate the model assumptions. 6.     Construct residual plots for checking outliers, leverage points and influential points. 7. Checking the assumption of homoscedasticity and its remedial measures  8. Detecting multicollinearity and its remedial measures Text Books And Reference Books:1. Chatterjee, S., & Hadi, A. S. (2015). Regression analysis by example. John Wiley & Sons. 2. Draper, N. R., & Smith, H. (2014). Applied regression analysis. 3rd edition. John Wiley & Sons. 3. Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis. John Wiley & Sons. Essential Reading / Recommended Reading1. Seber, G. A., & Lee, A. J. (2012). Linear regression analysis (Vol. 329). John Wiley & Sons. 2. Keith, T. Z. (2014). Multiple regression and beyond: An introduction to multiple regression and structural equation modelling. Routledge. 3. Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications. 4. Fox, J., & Weisberg, S. (2018). An R companion to applied regression. Sage publications. Evaluation PatternCIA - 50% ESE - 50% MST272 - STATISTICAL COMPUTING USING PYTHON (2021 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description Python is a generic programming language that is extensively used in data science. This course equips students with programming skill in Python and associated statistical libraries and to apply in data analysis Course Outcome CO1: Demonstrate the understanding of the fundamentals of Python programming.CO2: Implement functions and data modellingCO3: Analyze statistical datasets and visualize the resultsCO4: Build statistical models using various statistical libraries in python
 Unit-1 Teaching Hours:15 Introduction Installing Python - basic syntax - interactive shell - editing, saving  and  running  a script. The concept of data types -  variables -  assignments - mutable type - immutable types - arithmetic operators and expressions -  comments in the program - understanding error messages - Control statements - operators.    Practical Assignments: 1.  Lab exercise on data types 2.  Lab exercise on arithmetic operators and expressions  3. Lab exercise on Control statements Unit-2 Teaching Hours:15 Design with functions Introduction to functions - inbuilt and user defined functions - functions with arguments and return values - formal vs actual arguments - named arguments - Recursive functions -  Lambda function - OOP Concepts -  classes - objects - attributes and methods - defining classes - inheritance -  polymorphism.   Practical Assignments: 4.  Lab exercise on inbuilt and user-defined functions 5.  Lab exercise on Recursive and Lambda function  6. Lab exercise on OOP Concepts. Text Books And Reference Books:1.Lambert, K. A. (2018). Fundamentals of Python: first programs. Cengage Learning. 2.Haslwanter, T. (2016). An Introduction to Statistics with Python. Springer International Publishing. Essential Reading / Recommended Reading1.Unpingco, J. (2016). Python for probability, statistics, and machine learning, Vol.1, Springer International Publishing. 2.Anthony, F. (2015). Mastering pandas. Packt Publishing Ltd. Evaluation PatternCIA - 50% ESE - 50% MST273A - PRINCIPLES OF DATA SCIENCE AND DATA BASE TECHNIQUES (2021 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course provides a strong foundation for data science and the application area related to it and caters for the underlying core concepts and emerging technologies in data science. Course Outcome CO1: Explore the fundamental concepts of data scienceCO2: Apply data analysis techniques for handling large dataCO3: Demonstrate various databases and Compose effective queries
 Unit-1 Teaching Hours:15 Introduction to Data Science Introduction – Big Data and Data Science  – Data science Hype – Getting Past the Hype – The Current Landscape – Role of Data Scientist – Exploratory Data Analysis –  Data Science Process Overview – Defining goals – Retrieving data – Data preparation – Data exploration – Data modelling – Presentation. Problems in handling large data – General techniques for handling large data – Big Data and its importance, Four Vs, Drivers for Big data, Big data analytics, Big data applications, Algorithms using map-reduce, Matrix-Vector Multiplication by Map Reduce. Steps in big data – Distributing data storage and processing with Frameworks – Data science ethics – valuing different aspects of privacy – The five C’s of data.  Practical Assignments  1. Lab exercise for feature engineering    2. Lab exercise for big data processing Unit-2 Teaching Hours:15 Machine Learning Machine learning – Modeling Process – Training model – Validating model – predicting new observations – Supervised learning algorithms – Unsupervised learning algorithms. Introduction to deep learning – Deep Feed Forward networks – Regularization – Optimization of deep learning – Convolutional networks – Recurrent and recursive nets – applications of deep learning. Practical Assignments:  3.  Lab exercise on Linear and Logistic discrimination  4.  Lab exercise on K means clustering and Hierarchical clustering Text Books And Reference Books:1. Davy Cielen, Arno D. B. Meysman, Mohamed Ali (2016), Introducing Data Science, Manning Publications Co. 2. Thomas Cannolly and Carolyn Begg, (2007), Database Systems, A Practical Approach to Design, Implementation and Management”, 3rd Edition, Pearson Education. Essential Reading / Recommended Reading1. Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani (2013), An Introduction to Statistical Learning: with Applications in R, Springer. 2. D J Patil, Hilary Mason, Mike Loukides, (2018), Ethics and Data Science, O’Reilly. 3. LiorRokach and OdedMaimon, (2010), Data Mining and Knowledge Discovery Handbook. Evaluation PatternCIA - 50% ESE - 50% MST273B - SURVIVAL ANALYSIS (2021 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course will provide an introduction to the principles and methods for the analysis of time-to-event data. This type of data occurs extensively in both observational and experimental biomedical and public health studies. Course Outcome CO1: Explore the fundamental concepts of survival modelsCO2: Analyse survival data using various parametric modelsCO3: Identify Non-Parametric Survival techniques for applications lifetime dataCO4: Demonstrate the understanding of various Competing Risks and their effects
 Unit-1 Teaching Hours:15 Basic quantities and censoring The hazard and survival functions - Mean residual life function - competing risk - right,left and interval censoring, truncation - likelihood for censored and truncated data - Parametric and non-parametric estimation in truncated and censored cases. Practical Assignments: 1.Lab exercise on the parametric estimation of left and right-censored data 2.Lab exercise on the parametric estimation of truncated data 3.Lab exercise on the non-parametric estimation of censored and truncated data Unit-2 Teaching Hours:15 Parametric Survival Models Parametric forms and the distribution of log time - The exponential - Weibull - Gompertz - Gamma - Generalized Gamma - Coale-McNeil - and generalized F distributions - The U.S. life table - Approaches to modelling the effects of covariates - Parametric families - Proportional hazards models (PH) - Accelerated failure time models (AFT) - The intersection of PH and AFT. Proportional odds models (PO) - The intersection of PO and AFT - Recidivism in the U.S.  Practical Assignments: 1.Lab exercise on parametric modelling pf survival data 2.Lab exercise on the proportional hazard model 3.Lab exercise on AFT models Text Books And Reference Books:1. Klein, J. P., & Moeschberger, M. L. (2006). Survival analysis: techniques for censored and truncated data. Springer Science & Business Media.  2. Cleves, M.; W. G. Gould, and J. Marchenko (2016). An Introduction to Survival Analysis using Stata. Revised 3rd Ed. College Station, Texas: Stata Press.  3. Kalbfleisch, J. D., & Prentice, R. L. (2011). The statistical analysis of failure time data,2nd Ed. John Wiley & Sons.  4. Moore, D. F. (2016). Applied survival analysis using R. Switzerland: Springer. Essential Reading / Recommended Reading1. Singer, J.D and J. B. Willett (2003) Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford, Oxford University Press.  2. Therneau, T. M. and P. M. Grambsch (2000). Modelling Survival Data: Extending the Cox Model, Springer, NY 3. Collett, D. (2015). Modelling survival data in medical research. Chapman and Hall/CRC. Evaluation PatternCIA - 50% ESE - 50% MST273C - OPTIMIZATION TECHNIQUES (2021 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:100 Credits:4 Course Objectives/Course Description This course is designed to train the students to develop their modelling skills in mathematics through various methods of optimization. The course helps the students to understand the theory of optimization methods and algorithms developed for solving various types of optimization problems. Course Outcome CO1: Understand and apply linear programming problemsCO2: Apply one dimensional and multidimensional optimization problemsCO3: Understand multidimensional constrained and unconstrained optimization problemsCO4: Apply geometric and dynamic programming problemsCO5: Solve nonlinear problems through its linear approximation
 Unit-1 Teaching Hours:15 Linear Programming Problems (LPP) Introduction to optimization – convex set and convex functions – simplex method: iterative nature of simplex method – additional simplex method: duality concept - dual simplex method – generalized simplex algorithm - revised simplex method: revised simplex algorithm – development of the optimality and feasibility conditions.    Practical Assignments: 1. Formulate the LPP. 2. Solve the LPP using simplex method. 3. Solve the LPP using revised simplex method. Unit-2 Teaching Hours:15 Integer Linear Programming Branch and bound algorithm – cutting plane algorithm – transportation problem: north-west method, least-cost method, vogel’s approximation and method of multipliers – assignment problem: mathematical statement, Hungarian method, variations of assignment problems.  Practical Assignments: 4. Solve integer LPP by cutting plane method. 5. Formulate and solve transportation problems. 6. Formulate and solve assignment problems. Text Books And Reference Books: H. A. Taha (2017), Operations Research – An Introduction, 10th Edition, Prentice – Hall of India, New Delhi. S. S. Rao (2019), Engineering Optimization, 5th Edition, New Age International Pvt. Ltd., Publishers, Delhi. Essential Reading / Recommended Reading J.K. Sharma (2010), Quantitative Techniques for Managerial Decisions, Macmillan. Hadley, G. (2002), Linear Programming, Addison Wesley. G. Srinivasan (2007), Operations Research: Principles & Applications, Prentice Hall of India, New Delhi, India. Evaluation PatternCIA- 50% ESE-50% MST281 - RESEARCH PROBLEM IDENTIFICATION AND FORMULATION (2021 Batch) Total Teaching Hours for Semester:30 No of Lecture Hours/Week:2 Max Marks:50 Credits:1 Course Objectives/Course Description The course will be inculcating research culture which will enhance the employability skills to the students. Course Outcome CO1: Demonstrate the objective and data collection methodology for a research problem.
Unit-1
Teaching Hours:30
Problem Identification

Students will do the following,

1. Identify a domain for the research project

2. Literature survey

3. Identifying the existing methodology and models

4. Writing a problem statement

5. Project presentation at the end of the process

Text Books And Reference Books:

-

-

Evaluation Pattern

CIA - 50%

ESE - 50%

MST331 - STATISTICAL INFERENCE II (2020 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:4
Max Marks:100
Credits:4

Course Objectives/Course Description

 This course is designed to provide the strong conceptual foundations of testing of hypothesis, procedures of testing hypothesis, likelihood ratio tests, sequential tests, and non-parametric tests.

Course Outcome

CO1: Demonstrate the understanding of basic concepts of robust estimation and testing of hypotheses.

CO2: Apply the procedures of testing hypotheses for solving real-life problems.

CO3: Apply various non-parametric tests and draw conclusions to real-life problems.

CO4: Develop appropriate tests for testing specific statistical hypotheses.

CO5: Draw conclusions about the population with the help of various estimation and testing procedures.

Unit-1
Teaching Hours:14
Robust estimation

Robust estimation: The influence curve and empirical influence curve - M-estimation: Median, Trimmed and winsorized mean - Influence curve for M-estimators -  Limiting distribution of M-estimators - Resampling methods: Quenouille’s Jackknife estimation, parametric and non-parametric bootstrap methods.

Unit-2
Teaching Hours:10
Neyman-Pearson theory of testing of hypotheses

Basic concepts in statistical hypotheses testing - Simple and composite hypothesis - Critical regions - Type-I and Type-II error - Significance level - p-value and power of a test - Randomised and non-randomized tests - Neyman-Pearson lemma and its applications - Generalization of NP lemma - Construction of tests using NP lemma - Most powerful test - Uniformly most powerful test - Monotone Likelihood Ratio (MLR) property - Testing in one-parameter exponential families - Unbiased and invariant tests - Locally most powerful tests.

Text Books And Reference Books:

1. Rohatgi, V. K. and Saleh, A.K.M. (2015). An Introduction to Probability and

Statistics, John Wiley and Sons.

1.  Lehmann, E. L., and Romano, J. P. (2005). Testing Statistical Hypotheses, 2/e, John Wiley, New York.
1. Srivastava, M.K., Khan, A.H. and Srivastava, N. (2014). Statistical Inference- Testing of Hypothesis, Prentice Hall India, New Delhi.
2. Rajagopalan, M. and Dhanavanthan, P. (2012). Statistical Inference, PHI Learning Pvt Ltd, New Delhi.
3. Kendall, M.G. and Stuart, A. (1967). The Advanced Theory of Statistics, vol 2,

2nd edition. Mc-Millan, New York.

1. Kale, B. K. and Muralidharan, K.  (2015). Parametric Inference: An Introduction. Alpha Science Int. Ltd.
2. Mukhopadhyay, P.(2015): Mathematical Statistics, Books and Allied (P) Ltd., Kolkata.
3. Gibbons J.K. (1971).  Non-Parametric Statistical Inference, McGraw Hill.
Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST332 - MULTIVARIATE ANALYSIS (2020 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:4
Max Marks:100
Credits:4

Course Objectives/Course Description

The exposure provided to the multivariate data structure, multinomial and multivariate normal distribution, estimation and testing of parameters, various data reduction methods would help the students in having a better understanding of research data, its presentation and analysis. This course helps to understand multivariate data analysis methods and their applications in various research areas.

Course Outcome

CO1: Describe concepts of multivariate normal distribution.

CO2: Demonstrate the concepts of MANOVA and MANCOVA.

CO3: Identify various classification methods for multivariate data.

CO4: Analyze various data reduction methods for the multivariate data structure.

CO5: Interpret the results of various multivariate methods.

Unit-1
Teaching Hours:12
: Multivariate Distributions

Basic concepts on multivariate variables - Multivariate normal distribution - Marginal and conditional distribution - Concept of random vector - Its expectation and Variance - Covariance matrix. Marginal and joint distributions - Conditional distributions and Independence of random vectors - Multinomial distribution - Characteristic functions in higher dimensions - Multiple regressions and multiple correlations -Partial regression and Partial correlation (illustrative examples).

Unit-2
Teaching Hours:12
MANOVA and MANCOVA

Multivariate analysis of variance (MANOVA) and Covariance (MANCOVA) of one and two-way classified data with their interactions - Univariate and Multivariate Two-Way Fixed-effects Model with Interaction.

Text Books And Reference Books:

1. Anderson, T.W. (2004). An Introduction to Multivariate Statistical Analysis. John

Wiley. New York.

2. Johnson, R.A. and Wichern, D.W. (2018). Applied Multivariate Statistical Analysis.

6th edn. Prentice-Hall. London.

1. Rohatgi, V.K. and Saleh, A.K.M.E. (2015). An Introduction to Probability Theory and

Mathematical Statistics. 2nd edn. John Wiley & Sons. New York.

2. Srivastava, M.S. and Khatri, C.G. (1979). An Introduction to Multivariate Statistics.

North-Holland.

3. Muirhead, R.J. (1982). Aspects of Multivariate Statistical Theory. John Wiley. New

York.

Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST371 - TIME SERIES ANALYSIS (2020 Batch)

Total Teaching Hours for Semester:90
No of Lecture Hours/Week:6
Max Marks:150
Credits:5

Course Objectives/Course Description

The course considers statistical techniques to evaluate processes occurring through time. It introduces students to time series methods and the applications of these methods to different types of data in various fields. Time series modeling techniques including AR, MA, ARMA, ARIMA, and SARIMA will be considered with reference to their use in forecasting. The objective of this course is to equip students with various forecasting techniques and to familiarize themselves with modern statistical methods for analyzing time-series data.

Course Outcome

CO1: Demonstrate the understanding of basic concepts of analyzing time series, including white noise, trend, seasonality, cyclical component, autocovariance, and autocorrelation function.

CO2: Apply the concept of stationarity to the analysis of time-series data in various contexts.

CO3: Select the appropriate model, to fit parameter values, examine residual analysis, and carry out the forecasting calculation.

CO4: Apply various techniques of seasonal time series models, including the seasonal autoregressive integrated moving average (SARIMA) models and Winters exponential smoothing.

CO5: Demonstrate the principles behind modern forecasting techniques, which includes obtaining the relevant data and carrying out the necessary computation using R software.

 Unit-1 Teaching Hours:20 Basic concepts in time series analysis Stochastic Process - Time series as a discrete parameter stochastic process - Auto – Covariance - Autocorrelation and their properties - Exploratory time series analysis- graphical analysis - classical decomposition model - concepts of trend, seasonality and cycle - Estimation of trend and seasonal components-Elimination of trend and seasonality - Method of differencing - Moving average smoothing - Method of seasonal differencing Practical Assignments: 1.Graphical representation of time series, plots of ACF and PACF and their interpretation 2.Examples of  trend, seasonal and cyclical time series and estimation of trend and seasonal  components 3. Exercise on Moving average smoothing to eliminate trend and illustration on the method of differencing to eliminate trend and seasonality. 4.Exercise on least-square fitting to estimate and eliminate the trend component. Unit-2 Teaching Hours:20 Stationary time series models Stationary time series models - Concepts of weak and strong stationarity - General linear Process - Auto-Regressive(AR), Moving Average(MA), and Auto-Regressive Moving Average (ARMA) processes – their properties - conditions for stationarity and invertibility -model identification based on ACF and PACF- Maximum likelihood estimation - Yule Walker Estimation - order selection ( AIC and BIC ) - Residual Analysis- - Box Jenkins methodology to the identification of stationary time series models Practical Assignments: 5.Exercise on fitting AR model 6. Exercise on fitting MA model 7. Exercise on fitting ARMA model 8.Model-identification using ACF and PACF, Model selection using AIC and BIC 9. Residual analysis and diagnosis check for AR, MA, and ARMA models Text Books And Reference Books:1. Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis:     forecasting and control. John Wiley & Sons. 2. Chatfield, C., & Xing, H. (2019). The analysis of time series: an introduction with R. CRC Press. Essential Reading / Recommended Reading1. Hamilton, J. D. (2020). Time series analysis. Princeton university press. 2. Brockwell, P. J., & Davis, R. A. (2016). Introduction to time series and forecasting. springer. Evaluation PatternCIA - 50% ESE - 50% MST372A - STATISTICAL MACHINE LEARNING (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description Machine learning has a wide array of applications that belongs to different fields, such as biomedical research, reliability of large structures, space research, digital marketing, etc. This course will equip students with a wide variety of models and algorithms for machine learning and prepare students for research or industry application of machine learning techniques. Course Outcome CO1: Demonstrate the understanding of basic concepts of statistical machine learningCO2: Apply classification algorithms for qualitative data.CO3: Analyze high dimensional data using principal component regression learning algorithmsCO4: Construct classification and regression trees by random forestsCO5: Create a statistical learning model using support vector machines
 Unit-1 Teaching Hours:15 Statistical learning Statistical learning: definition-prediction accuracy and model interpretability-supervised and unsupervised learning-assessing model accuracy- important problems in data mining: classification, regression, clustering, ranking, density estimation- Concepts: training and testing, cross-validation, overfitting, bias/variance tradeoff, regularized learning equation- simple and multiple linear regression algorithms.   Practical Assignments:   1.     Lab exercise on data preparation and using simple linear regression   2.     Lab exercise on model assessment simple linear regression   3.     Lab exercise on data preparation with multiple linear regression Unit-2 Teaching Hours:15 Classification algorithms Logistic model- training and testing the model-linear discriminant analysis-quadratic discriminant analysis- Use of Bayes’ theorem-k- nearest neighbours - Naive Bayes’- Adaboost.   Practical Assignments:   4.     Lab exercise on the logistic model   5.     Lab exercise on discriminant analysis   6.     Lab exercise on  Naïve Bayes’ and k-NN classifiers Text Books And Reference Books: James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, p. 18). New York: springer. Essential Reading / Recommended Reading Gutierrez, D. D. (2015). Machine learning and data science: an introduction to statistical learning methods with R. Technics Publications. Müller, A. C., & Guido, S. (2016). Introduction to machine learning with Python: a guide for data scientists. “O’Reilly Media, Inc.". Murphy, K. P. (2012). Machine learning: a probabilistic perspective. MIT press Evaluation PatternCIA - 50% ESE - 50% MST372B - BIOSTATISTICS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course provides an understanding of various statistical methods in describing and analyzing biological data. Students will be equipped with an idea about the applications of statistical hypothesis testing,  related concepts and interpretation in biological data. Course Outcome CO1: Demonstrate the understanding of basic concepts of biostatistics and the process involved in the scientific method of research.CO2: Identify how the data can be appropriately organized and displayed.CO3: Interpret the measures of central tendency and measures of dispersion.CO4: Interpret the data based on the discrete and continuous probability distributions.CO5: Apply parametric and non-parametric methods of statistical data analysis.
 Unit-1 Teaching Hours:15 Introduction to Biostatistics Presentation of data - graphical and numerical representations of data - Types of variables, measures of location - dispersion and correlation - inferential statistics - probability and distributions - Binomial, Poisson, Negative Binomial, Hyper geometric and normal distribution.   Practical Assignments: Exercise on the representation of data Exercise on reporting data by descriptive statistics Unit-2 Teaching Hours:15 Parametric and Non - Parametric methods Parametric methods - one sample t-test -  independent sample t-test - paired sample t-test - one-way analysis of variance - two-way analysis of variance - analysis of covariance - repeated measures of analysis of variance - Pearson correlation coefficient - Non-parametric methods: Chi-square test of independence and goodness of fit - Mann Whitney U test - Wilcoxon signed-rank test - Kruskal Wallis test - Friedman’s test - Spearman’s correlation test.   Practical Assignments: Exercise on various parametric methods of analysis Exercise on various non-parametric methods of analysis Text Books And Reference Books: Marcello Pagano and Kimberlee Gauvreau (2018), Principles of Biostatistics, 2nd Edition, Chapman and Hall/CRC press David Moore S. and George McCabe P., (2017) Introduction to practice of statistics, 9th Edition, W. H. Freeman. Sundar Rao and Richard J., (2012) Introduction to Biostatistics and research methods, PHI Learning Private limited, New Delhi. Essential Reading / Recommended Reading Abhaya  Indrayan and Rajeev Kumar M., (2018) Medical Biostatistics, 4th Edition, Chapman and Hall/CRC Press. Gordis Leon (2018), Epidemiology, 6th Edition, Elsevier, Philadelphia Ram, F. and Pathak K. B., (2016): Techniques of Demographic Analysis,Himalaya Publishing house, Bombay. Park K., (2019), Park's Text Book of Preventive and Social Medicine, Banarsidas Bhanot, Jabalpur. Evaluation Pattern50% Continuous Internal Asssessssment (CIA). 50% End Semester Examination. MST372C - RELIABILITY ENGINEERING (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course will provide knowledge in different probability models in the reliability evaluation of the system and its components. Reliability engineering is applied in the industry to reduce failures, ensure effective maintenance and optimize repair time. Course Outcome CO1: Demonstrate the understanding of basic concepts of reliability.CO2: Analyze system reliability using probability models.CO3: Evaluate reliability from the lifetime data using common estimation proceduresCO4: Create a stress-strength model for system reliability.
 Unit-1 Teaching Hours:15 Basic concepts Reliability of a system - failure rate - mean, variance and percentile residual life: identities connecting them - notions of ageing - IFR, IFRA, NBU, NBUE, DMRL, HNBUE, NBUC, etc. and their mutual implications - TTT transforms and characterization of ageing classes.   Practical Assignments: Exercise on failure rate function and mrl function Exercise on comparison ageing classes Unit-2 Teaching Hours:15 Lifetime models Non-monotonic failure rates and mean residual life functions - study of lifetime models: exponential, Weibull, lognormal, generalized Pareto, gamma with reference to basic concepts and ageing characteristics - bathtub and upside-down bathtub failure rate distributions   Practical Assignments:       3. Exercise on exponential lifetime model       4. Exercise on Weibull lifetime model       5. Exercise on bathtub shaped lifetime model Text Books And Reference Books:1.      Birolini, A. (2013). Reliability engineering: theory and practice. Springer Science & Business Media.. 2.      Bain, L. (2017). Statistical analysis of reliability and life-testing models: theory and methods. Routledge. Essential Reading / Recommended Reading Barlow, R. E., & Proschan, F. (1975). Statistical theory of reliability and life testing: probability models. Florida State Univ Tallahassee. Tobias, P. A., & Trindade, D. (2011). Applied reliability. CRC Press. Evaluation PatternCIA - 50% ESE - 50% MST373A - NUMERICAL ANALYSIS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course deals with the theory and application of different numerical methods techniques to solve the complex problems that arise in the modern world of science. The course highlights that through the numerical algorithms, it is definite to arrive at a solution which is efficient and stable for large scale systems. Course Outcome CO1: Demonstrate the understanding of floating-point numbers and the role of errors and their analysis in numerical methods.CO2: Identity accuracy, consistency, stability, and convergence of numerical methods.CO3: Derive numerical solutions of the algebraic and transcendental equations, ordinary differential equations, and boundary value problems.CO4: Interpret, analyse and evaluate results from numerical computations.
 Unit-1 Teaching Hours:15 Error analysis and basics of the solution of algebraic equations Errors and their analysis – Floating Point representation of numbers – Solution of algebraic and Transcendental equations: Bisection method, fixed-point iteration method, the method of False position, Newton Raphson method and Muller’s method. The solution of linear systems – Matrix inversion method – Gauss elimination method – Gauss-Seidel and Gauss-Jacobi iterative methods. Practical Assignments: 1. Solutions to algebraic equations using Bisection and fixed point methods 2. Solutions to algebraic and transcendental equations using Newton Raphson and Muller’s method. 3. Solving system of linear equations using Matrix inversion and Gauss elimination methods 4. Finding real roots to a system of linear equations using Gauss-Seidel and Gauss-Jacobi iterative methods. Unit-2 Teaching Hours:15 Advanced methods to Solve algebraic and transcendental equations Convergence criterion, Aitken’s-process - Sturm sequence method to identify the number of real roots, Bairstow’s method - Graeffe’s root squaring method - Birge-Vieta method - Solution of Linear system of algebraic equations: LU-decomposition methods (Crout’s, Cholesky and Delittle methods), consistency and ill-conditioned system of equations, Tridiagonal system of equations, Thomas algorithm.    Practical Assignments:   5. Identifying real roots for algebraic equations using the Sturm sequence method and Bairstow’s method.   6. Solving equations using the Birge-Vieta method.   7. Solving system of linear equations using LU decomposition methods.   8. Examining consistency of the system of equations using Tridiagonal system of equations and Thomas algorithm. Text Books And Reference Books: C. F. Gerald and P. O. Wheatley, Applied Numerical Analysis, 7th Edition, Pearson publications, reprint 2017. M. K. Jain, Iyengar, S. R. K. and R. K. Jain, Numerical Methods Problems and Solutions, 3rd Editions,  New Age Pvt. Pub, New Delhi, reprint 2020. Essential Reading / Recommended Reading1.      R.L. Burden and J. Douglas Faires, Numerical Analysis, 9th Edition, Boston: Cengage Learning, 2011. 2.      S.C. Chopra and P.C. Raymond, Numerical Methods for Engineers, New Delhi: Tata McGraw-Hill, 2010. 3.      Graham. W Griffiths, Numerical Analysis using R solution to ODEs and PDEs, Cambridge University Press, 2016. 4.      Jaan Kiusalaas, Numerical methods in Engineering with Python 3, Cambridge University Press, 2013. Evaluation PatternCIA - 50% ESE- 50% MST373B - NON-PARAMETRIC METHODS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course will provide the basic theory and computing tools to perform nonparametric tests, including the Sign test, Wilcoxon signed-rank test, Median test etc. Kruskal-Wallis for one-way and multiple comparisons, linear rank test for location and scale parameters and measure of association in bivariate populations are other nonparametric tests covered in this course. The aim of the course is the in-depth presentation and analysis of the most common methods and techniques of non-parametric statistics such as sign test, rank test, run test, median test etc. Course Outcome CO1: Compare different nonparametric hypothesis tests in two-sample problems.CO2: Construct interval estimators for population medians and other population parameters based on rank-based methods.CO3: Formulate, test, and interpret various hypothesis tests for location, scale, and independence problemsCO4: Demonstrate different measures of association for bivariate samples.
 Unit-1 Teaching Hours:15 One-Sample and Paired-Sample Procedures The quantile function - the empirical distribution function - statistical properties of order statistics- confidence interval for a population quantile -hypothesis testing for a population quantile -the sign test and confidence interval for the median - rank-order statistics -treatment of ties in rank tests-  Wilcoxon signed-rank test and confidence interval   Practical Assignments:   Exercise on confidence interval estimation and hypothesis test for a population Quantile Exercise on sign test and confidence interval for the median Exercise on rank-order statistics -treatment of ties in rank tests Exercise on Wilcoxon signed-rank test and confidence interval Unit-2 Teaching Hours:15 The General two-sample problem Wald-Wolfowitz runs test - Kolmogorov-Smirnov two-sample test - median test - the control median test - the Mann-Whitney U test                                                                                       Practical Assignments:  5.Exercise on Wald-Wolfowitz runs test 6.Exercise on Kolmogorov-Smirnov two-sample test. 7.Exercise on Median test and control median test.   8.Exercise on Mann-Whitney U test. Text Books And Reference Books: Gibbons, J. D., & Chakraborti, S. (2020). Nonparametric statistical inference. CRC press. Kloke, J., & McKean, J. W. (2014). Nonparametric statistical methods using R. CRC Press. Essential Reading / Recommended Reading  Hollander, M., Wolfe, D. A., & Chicken, E. (2013). Nonparametric statistical methods (Vol. 751). John Wiley & Sons. Lewis, N. D. C. (2013). 100 Statistical Tests in R. Heather Hills Press. Evaluation PatternCIA 50% ESE 50% MST373C - THEORY OF GAMES AND STATISTICAL DECISIONS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description Game theory and the decision is a branch of Mathematics and Statistics that enables to study of the strategic interactions amongst rational decision-makers. Traditionally, game-theoretic tools have been applied to solve problems in Economics, Business, Political Science, Biology, Sociology, Computer Science, Logic, and Ethics. In recent years, applications of game theory have been successfully extended to several areas of engineered / networked system such as wireline and wireless communications, static and dynamic spectrum auction, social and economic networks. Course Outcome CO1: Demonstrate the basics of a ?game? and translate the basics of a ?game? into a wide range of conflicts.CO2: Apply the minimax, randomized, and non-randomized decision rules to real-life problems.CO3: Infer the importance of rules based on sufficient and essentially complete class.CO4: Identify the invariant statistical decision problems and their solutionsCO5: Apply the Bayes rules in multiple decision problems and address Slippage problems.
 Unit-1 Teaching Hours:15 Game and Decision Theories Theory of games - zero-sum game - minimax - maxmin -  dominance strategy - the value of the game - Basic elements of game and Decision -  Comparison of the two theories - Decision function and Risk function; Randomization and optimal decision rules - Form of Bayes rules for estimation.                                                                                                          Practical Assignments: Two-person zero-sum game Game with minimax and maximin strategies Game with dominance rule and value of the game. Unit-2 Teaching Hours:15 Main Theorems of Decision Theory Admissibility and completeness - Fundamental theorems of Game and Decision theories - Admissibility of Bayes rules - Existence of Bayes decision rules - Existence of minimal complete class - Essential completeness of the class of non-randomized decision rules - Minimax theorem -  The complete class theorem -  Methods for finding minimax rules.                      Practical Assignments: Admissibility of Bayes rules Examining the completeness Problems on the non-randomized decision rule Text Books And Reference Books: William M. Bolstad (2007), Introduction to Bayesian Statistics, 2 nd Edition.  J.O. Berger (1985), Statistical Decision Theory and Bayesian Analysis, 2 nd Edition, Springer      . Essential Reading / Recommended Reading   Robert Winkler (Jan 15, 2003) An Introduction to Bayesian Inference and Decision, Second  Edition. T.S. Ferguson (1967), Mathematical Statistics – A Decision Theoretic, Approach,  Academic Press. M.H. DeGroot (1976), Optimal Statistical Decisions, McGraw Hill. Evaluation PatternCIA - 50% ESE - 50% MST381 - RESEARCH MODELING AND IMPLEMENTATION (2020 Batch) Total Teaching Hours for Semester:120 No of Lecture Hours/Week:8 Max Marks:200 Credits:4 Course Objectives/Course Description This will equip the student to apply statistical methods they have studied in various courses and present their work through research articles. Course Outcome CO1: Apply statistical techniques to a real-life problem.CO2: Interpret and conclude the statistical analysis scientifically.CO3: Present the work done through presentation and research article.
 Unit-1 Teaching Hours:120 Modelling and Implementation 1. Apply various statistical methods in solving a real-life problem. 2. Comparison with the existing models or results. 3. Writing research article  4. Presentation of the article Text Books And Reference Books:_ Essential Reading / Recommended Reading_ Evaluation PatternCIA 50% ESE 50% MST431 - ADVANCED OPERATIONS RESEARCH (2020 Batch) Total Teaching Hours for Semester:60 No of Lecture Hours/Week:4 Max Marks:100 Credits:4 Course Objectives/Course Description Operations research helps in solving problems in different environments that need decisions. The module includes the topics : linear programming, integer programming, nonlinear programming, simple queueing models and inventory models. The aim of the course is to provide the students, how to formulate the problems into mathematical models and to use the appropriate methods to solve them. Course Outcome CO1: Understand mathematical models used in Operations Research and use solution methods such as Simplex, revised simplex, and dual simplex for solving linear programming problems.CO2: Solve integer programming models using Cutting plane and brand and bound methods.CO3: Solve non-linear programming problems with equality and inequality constraints.CO4: Analyze service-oriented problems using queuing models.CO5: Understand the methods used by organizations to obtain the right quantities of stock or inventory, as well as familiarize themselves with inventory management practices.
Unit-1
Teaching Hours:12
Linear Programming problem (LPP)

General Linear programming problem - Formulation -  Solution through graphical, Simplex, Big-M and Two phase methods - Revised Simplex method - Big-M and Two phase Revised Simplex methods - Duality - Primal-dual relationships - Dual Simplex method.

Unit-2
Teaching Hours:12
Integer Programming

Gomory’s All-Integer Cutting-Plane Method - Construction of Gomory’s Constraint - Gomory’s Mixed-Integer Cutting-Plane Method -  Construction of Additional Constraint for Mixed-Integer Programming Problem - Branch and Bound Method.

Text Books And Reference Books:

1. Bhunia, A. K., Sahoo, L., & Shaikh, A. A. (2019). Advanced Optimization and Operations Research. Springer.

1. Srinivasan, G. (2017). Operations Research: principles and applications. PHI Learning Pvt. Ltd.

2. Taha, H. A. (2013). Operations research: an introduction. Pearson Education India.

3. Shortle, J. F., Thompson, J. M., Gross, D., & Harris, C. M. (2018). Fundamentals of queueing theory (Vol. 399). John Wiley & Sons.

4. Sharma, J. K. (2016). Operations research: theory and applications. Trinity Press, an imprint of Laxmi Publications Pvt. Limited.

Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST432 - DESIGN AND ANALYSIS OF EXPERIMENTS (2020 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:4
Max Marks:100
Credits:4

Course Objectives/Course Description

This course will provide students with a mathematical background of various basic designs involving one-way and two-way elimination of heterogeneity and characterization properties. To prepare the students in deriving the expressions for analysis of experimental data and selection of appropriate designs in planning a scientific experimentation

Course Outcome

CO1: Demonstrate basic principles and characterization properties of various designs of the experiment.

CO2: Identify appropriate design of experiments to solve research problems of various domains.

CO3: Design factorial experiments with confounding.

CO4: Construct split and strip plot designs.

CO5: Analyze the Incomplete Block designs.

Unit-1
Teaching Hours:12
Basic of design of experiments

Basic principles of design of experiments - Randomization - Replication and Local control - Uniformity trials - Size and Shape of plots and blocks - Elements of linear estimation - Analysis of variance - Completely Randomized Design (CRD) - Randomized Complete Block Design (RCBD) and Latin Square Design (LSD) -  Missing plot techniques

Unit-2
Teaching Hours:12
Analysis of Covariance

Analysis of covariance - Ancillary/Concomitant variable and study variable - Linear model for ANCOVA - Adjustment of treatment sum of squares in ANCOVA - One - Way and two-way classification with a single concomitant variable in CRD and RCBD designs.

Text Books And Reference Books:
1. Montgomery, D.C. (2019). Design and Analysis of Experiments. John Wiley and Sons, Inc. New York
1. Gupta, S.C and Kapoor, V.K. (2019). Fundamentals of Applied Statistics. 4th edition (Reprint). Sultan Chand and Sons. India.
2. Cochran, W.G. and Cox, G.M. (1992). Experimental Designs. John Wiley.
3. Dean, A.M. and Voss, D. (1999). Design and Analysis of Experiments. Springer.
4. Das, M.N. and Giri, N.C. (1986). Design and Analysis of Experiments. New Age.
5. Lawson, J. (2015). Design and Analysis of Experiments with R. CRC Press
6. Dey, A. (1986). Theory of Block Designs. Wiley Eastern Ltd.

Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST433 - STATISTICAL QUALITY CONTROL (2020 Batch)

Total Teaching Hours for Semester:60
No of Lecture Hours/Week:4
Max Marks:100
Credits:4

Course Objectives/Course Description

This course provides an introduction to the application of statistical tools in the industrial environment to study, analyze and control the quality of products

Course Outcome

CO1: Understand concepts of control charts in quality improvement

CO2: Analyze process capability using control charts

CO3: Construct modified control charts to monitor the process

CO4: Evaluate the quality of products using various acceptance sampling plans

Unit-1
Teaching Hours:12
Statistical Process Control

Meaning and scope of statistical quality control - Causes of quality variation - Control charts for variables and attributes - Rational subgroups - Construction and operation of, σ, R, np, p, c and u charts - Operating characteristic curves of control charts. Process capability analysis using histogram, probability plotting and control chart - Process capability ratios and their interpretations.

Unit-2
Teaching Hours:12

Specification limits and tolerance limits - Modified control charts - Basic principles and design of cumulative - sum control charts – Concept of V-mask procedure – Tabular CUSUM charts - Construction of Moving range - moving-average and geometric moving-average control charts.

Text Books And Reference Books:

1. Montgomery, D. C. (2019). Introduction to Statistical Quality Control, Eighth Edition, Wiley India, New Delhi.

1 Juran, J.M., and De Feo, J.A. (2010). Juran’s Quality control Handbook – The Complete Guide to Performance Excellence, Sixth Edition, Tata McGraw-Hill, New Delhi.

2. Schilling, E. G., and Nuebauer, D.V. (2009). Acceptance Sampling in Quality Control, Second Edition, CRC Press, New York

3. Duncan, A. J. (2003.). Quality Control and Industrial Statistics, Irwin-Illinois, US.

Evaluation Pattern
 Component Marks CIA I 10 Mid Semester Examination (CIA II) 25 CIA III 10 Attendance 05 End Semester Exam 50 Total 100

MST471A - NEURAL NETWORKS AND DEEP LEARNING (2020 Batch)

Total Teaching Hours for Semester:75
No of Lecture Hours/Week:5
Max Marks:150
Credits:4

Course Objectives/Course Description

The objective of this course is to provide fundamental knowledge of neural networks and deep learning. This course gives a brief idea of the basics of neural networks, shallow and deep neural networks and other methods to build various research projects.

Course Outcome

CO1: Identify the difference between biological and arithmetic neural networks.

CO2: Demonstrate the different types of supervised learning algorithms.

CO3: Build and train various Convolution Neural Networks

CO4: Implement Recurrent Neural Networks and other artificial neural networks for real-time applications.

 Unit-1 Teaching Hours:15 Introduction to Artificial Neural Networks Fundamental concepts of Artificial Neural Networks (ANN) - Biological neural networks - Comparison between biological neuron and artificial neuron - Evolution of neural networks - Scope and limitations of ANN - Basic models of ANN - Learning methods - Activation functions - Important terminologies of ANN: Weights - Bias - Threshold - Learning Rate - Momentum factor - Vigilance parameters. Practical  Assignments: Exercise on construction of Artificial Neural Networks. Exercise on training and testing the data Unit-2 Teaching Hours:15 Supervised Learning Algorithms Concept of supervised learning algorithms - Perceptron networks - Adaptive linear neuron (Adaline) - Multiple adaptive linear neuron - Back-Propagation network: Learning factors - Initial weights - Learning rate ɑ - Momentum factor - Generalization - Training and testing of the data. Practical  Assignments:  3. Exercise on multiple adaptive linear neurons 4. Exercise on Back-propagation networks Text Books And Reference Books: Charu C. Aggarwal (2018) Neural Networks and Deep Learning A Textbook, Springer International Publishing, Switzerland. Essential Reading / Recommended Reading S.N Sivanandam, S.N Deepa (2018). Principles of soft computing. Wiley India. S Lovelyn Rose, L Ashok Kumar, Karthika Renuka (2019). Deep Learning using Python. Wiley India. Francois Chollet (2017). Deep Learning with Python. Manning Publishing. Andreas C. Muller & Sarah Guido (2017). Introduction to Machine Learning with Python. O’Reilly Media, Inc. Evaluation PatternCIA - 50% ESE - 50% MST471B - SPATIAL STATISTICS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course has been conceptualized in order to understand the fundamental and applied concepts of spatial statistics that describe the diverse set of methods to model and analyze the various types of Spatial data. Course Outcome CO1: Demonstrate an understanding of the fundamental concepts of spatial statistical analysis.CO2: Identify the various types of spatial data by plots.CO3: Apply the appropriate statistical model to the various types of spatial data.CO4: Analyze and interpret the spatial data problems of various disciplines.
 Unit-1 Teaching Hours:15 Introduction to spatial statistics Spatial data - Types of spatial data- Geostatistical data, Lattice data, Point pattern data with examples  - Visualizing spatial data: Traditional plots, lattice plots and interactive plots – Exploratory spatial data analysis - Intrinsic stationarity, Square-Root-Differences Cloud -  The Pocket plot – Decomposing the data into large and small scale variation -  Analysis of residuals – Variogram of residuals. Practical Assignments:   Exercise on the visualization of spatial data using traditional plots,  Exercise on the visualization of spatial data using lattice and interactive plots Exercise on exploratory data analysis Unit-2 Teaching Hours:15 Geostatistical data Stationary Processes: Variogram, Covariogram and Correlogram - Estimation of variogram: Comparison of the variogram and covariogram estimation, exact distribution theory of the variogram - Robust estimation of variogram –  Spectral representations: Valid covariograms and variograms - Variogram model fitting: Criteria for fitting a variogram model, properties of variogram-parameter estimators, Cross-validating the fitted variogram. Practical Assignments:   Exercise on exploratory variogram analysis Exercise on variogram Exercise on variogram modelling  Exercise on residual variogram modeling Text Books And Reference Books:1. Cressie, Noel A.C. (2015). Statistics for Spatial Data. Revised Edition. Wiley Interscience Publication. Essential Reading / Recommended Reading1. Bivand Roger S., Pebesma Edzer J.  and Gomez-Rubio V. (2013). Applied Spatial Data Analysis with R. Springer New York(2nd Edition). Evaluation PatternCIA 50%+ESE 50% MST471C - BIG DATA ANALYTICS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course has been designed to train the students in handling different types of Big data sets and provide knowledge about the methods of handling these types of data sets. Course Outcome CO1: Demonstrate the understanding of basic concepts of Big dataCO2: Identify different types of Hadoop architectureCO3: Illustrate the parallel processing of data using MapReduce techniquesCO4: Analyze the Big data under Spark architectureCO5: Demonstrate the programming of Big data using Hive and Pig environments
 Unit-1 Teaching Hours:15 Introduction Concepts of Data Analytics: Descriptive, Diagnostic, Predictive, Prescriptive analytics -Big Data characteristics: Volume, Velocity, Variety, Veracity of data - Types of data: Structured, Unstructured, Semi-Structured, Metadata - Big data sources: Human-Human communication, Human-Machine Communication, Machine-Machine Communication - Data Ownership - Data Privacy. Practical Assignments: 1. Setting up infrastructure and Automation environment 2. Case study for identifying Data Characteristics Unit-2 Teaching Hours:15 Big Data Architecture Standard Big data architecture - Big data application - Hadoop framework - HDFS Design goal - Master-Slave architecture - Block System - Read-write Process for data - Installing HDFS - Executing in HDFS: Reading and writing Local files and Data streams into HDFS - Types of files in HDFS - Strengths and alternatives of HDFS - Concept of YARN.   Practical Assignments: 3.  Exercise on Installing HDFS 4.  Exercise on Reading and Writing Local files into HDFS 5.  Exercise on Reading and Writing Data streams into HDFS Text Books And Reference Books: Anil Maheshwari (2020). Big Data. 2nd Edition. McGraw Hill Education Pvt Ltd. Essential Reading / Recommended Reading Thomas Erl, Wajid Khattak and Paul Buhler (2016). Big Data Fundamentals: Concepts, Drivers and Techniques. Service Tech Press. Julián Luengo, Diego García-Gil, Sergio Ramírez-Gallego, Salvador García, Francisco Herrera (2020). Big Data Preprocessing: Enabling Smart Data. Springer Nature Publishing. Seema Acharya, Subhasini Chellappan (2019), Big Data and Analytics. 2nd Edition, Wiley India Pvt Ltd. Evaluation PatternCIA - 50% ESE - 50% MST472A - HIGH DIMENSIONAL STATISTICAL ANALYSIS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course has been conceptualized in order to understand the high dimensional data and the statistical techniques such as principal component analysis, multidimensional scaling, independent component analysis and projection pursuit that are used to analyze the most challenging multidimensional real life problems. Course Outcome CO1: Identify high-dimensional problems in various domains.CO2: Select the appropriate statistical techniques to analyze high-dimensional data.CO3: Apply the various statistical techniques to analyze the high-dimensional real-life problems.CO4: Interpret the results obtained by high dimensional statistical analysis in the context of real-world problems.
 Unit-1 Teaching Hours:12 Unit I: Understanding high dimensional data Introduction to high dimensional data: high dimensional data in various fields with examples - need of high dimensionality - Curse and blessings of Dimensionality - Visualization of multidimensional data - parallel coordinate plots - multivariate random vectors - Multivariate normal distribution and estimation of parameters using likelihood estimation.                                                                            Practical Assignments: 1.   Exercise on visualization of high dimensional data       2.  Exercise on multivariate normal distribution Unit-2 Teaching Hours:18 Principal component analysis in high dimensions Principal component analysis - Principal components and dimension reduction - Visualization of principal components - Scree, Score, Projection plots and estimates of the density of the scores - Properties of principle components - Uses and interpretation of principal components - Standardized and high dimensional data - Sparse principal component analysis with LASSO and elastic nets - Consistency of principal components as the dimension grows.   Practical Assignments:                                             3.         Exercise on the identification of principal components.   4.         Exercise on projection plots.   5.         Exercise on sparse principal component analysis based on LASSO.   6.         Exercise on sparse principal component analysis based on elastic nets. Text Books And Reference Books:      1.   Inge Koch (2013). Analysis of multivariate and high-dimensional data. Cambridge University Press Essential Reading / Recommended ReadingWainwright, Martin, J. (2019). High-Dimensional Statistics-A Non-Asymptotic Viewpoint. Cambridge University Press. 2.     Giraud, C. (2014).  Introduction to High-Dimensional Statistics. CRC Press. Evaluation PatternCIA-50% ESE-50% MST472B - STATISTICAL GENETICS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description To enable the students to understand and apply different concepts of statistical genetics in large populations with selection, mutation and migration. The students would be exposed to the physical basis of inheritance, detection and estimation of linkage, estimation of genetic parameters and development of selection indices. Course Outcome CO1: Describe basic concepts of estimation of linkage and segregation in large populations.CO2: Demonstrate the effect of systematic forces on change of gene frequency.CO3: Estimate genetic variance and analyze its partitioningCO4: Apply statistical methodology to estimate the correlation between relatives and selection indexCO5: Interpret the results of various statistical genetics techniques.
 Unit-1 Teaching Hours:15 Segregation and Linkage Physical basis of inheritance - Analysis of segregation - Detection and Estimation of linkage for qualitative characters - Amount of information about linkage - Combined estimation - Disturbed segregation. Practical Assignments: 1.      Analysis of segregation, detection and estimation of linkage. 2.      Estimation of Amount of information about linkage. 3.      Calculation of combined estimationof linkage. Unit-2 Teaching Hours:15 Equilibrium law and Sex-Linked gene Gene and genotypic frequencies - Random mating and Hardy-Weinberg law - Application and extension of the equilibrium law - Fisher’s fundamental theorem of natural selection - Disequilibrium due to linkage for two pairs of genes - Sex - Linked genes. Practical Assignments: 4. Estimation of disequilibrium due to linkage for two pairs of genes. 5. Estimation of path coefficients. 6. Estimation of equilibrium between forces in large populations. Text Books And Reference Books:1. Jain, J.P. (2017). Statistical Techniques in Quantitative Genetics. Tata McGraw Essential Reading / Recommended Reading1.Laird N.M and Christoph, L. (2011). The Fundamental of Modern Statistical Genetics. Springer. 2. Balding DJ, Bishop, M. and Cannings, C. (2001). Handbook of Statistical Genetics. John Wiley. 3. Shizhong Xu.(2013). Principles of Statistical Genomics. Springer. 4.Falconer, D.S. (2009). Introduction to Quantitative Genetics. English Language Book Society. Longman. Essex. Evaluation PatternCIA - 50 % ESE- 50 % MST472C - ACTUARIAL METHODS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course is designed to equip students with the knowledge of actuarial models and their applications Course Outcome CO1: Demonstrate the understanding of basic concepts of actuarial methodsCO2: Identify various actuarial models.CO3: Illustrate survival models and life tables.CO4: Interpret the real-life data based on exploratory data analysis.CO5: Apply actuarial models to real-life data.
 Unit-1 Teaching Hours:15 Introduction to actuarial statistics Utility theory-introduction - insurance and utility theory - models for individual claims and their sums - curtate future lifetime - the force of mortality -assumptions for fractional ages - some analytical laws of mortality - multiple life functions - joint life and last survivor status - insurance and annuity benefits through multiple life functions - evaluation for special mortality laws. Practical Assignments: 1.      Problems based on multiple life functions 2.      Illustrate discrete and continuous annuity benefits Unit-2 Teaching Hours:15 Survival analysis and life tables Introduction to survival analysis - life table and its relation with survival function - examples - assumptions for fractional ages - estimate empirical survival and loss distribution using Kaplan-Meier estimator - Nelson Aalen estimator - Cox proportional hazards and Kernel density estimators. Practical Assignments: 3. Apply survival models to simple problems in long-term insurance, pensions and banking. 4. Preparation of life tables based on the real life data. 5. Estimation of survival distribution using Kaplan-Meier estimator, Nelson Aalen estimator, Cox proportional hazards and Kernel density estimators Text Books And Reference Books: N.L. Bowers, H.U. Gerber, J.C. Hickman, D.A. Jones and C.J. Nesbitt, (2014), Actuarial Mathematics, Society of Actuaries, Ithaca, Illinois, U.S.A. Essential Reading / Recommended Reading1.         Zdzislaw Brzezniak and Tomasz Zastawniak (2000), Basic stochastic processes: A course through exercises. Springer. 2.         Grimmett Geoffery and David Stizaker (2001), Probability and random processes. Oxford University Press. 3.         J. Medhi, Stochastic Processes (2009), John Wiley. Evaluation PatternCIA - 50% ESE - 50% MST473A - BAYESIAN STATISTICS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description Students who complete this course will gain a solid foundation in how to apply and understand Bayesian statistics and how to understand Bayesian methods vs frequentist methods.  Topics covered include: an introduction to Bayesian concepts; Bayesian inference for binomial proportions, Poisson means, and normal means; modelling Course Outcome CO1: Identify Bayesian methods for a binomial proportion and a Poisson meanCO2: Perform Bayesian analysis for differences in proportions and meansCO3: Analyze normally distributed data in the Bayesian frameworkCO4: Evaluate posterior distribution using various sampling procedures.CO5: Compare Bayesian methods and frequentist methods
 Unit-1 Teaching Hours:15 Introduction to Bayesian Thinking Basics of minimaxity - subjective and frequentist probability - Bayesian inference -  prior distributions - posterior distributions -  loss function - the principle of minimum expected posterior loss - quadratic and other common loss functions - advantages of being Bayesian - Improper priors - common problems of Bayesian inference - Point estimators - Bayesian confidence intervals, testing - credible intervals  Practical Assignments: 1.Construction of prior, conditional and posterior probabilities for the chosen data set 2.Computation minimum expected posterior loss. 3.Computation of Bayesian confidence intervals. Unit-2 Teaching Hours:15 Bayesian Inference for Discrete Random Variables Two Equivalent Ways of Using Bayes' Theorem - Bayes' Theorem for Binomial with Discrete Prior - Important Consequences of Bayes' Theorem - and Bayes' Theorem for Poisson with Discrete prior. Practical Assignments: 4.Bayes Classification  5.Examples of Binomial distribution with discrete prior. 6.Examples of Poisson distribution with discrete prior. Text Books And Reference Books:1. Bolstad W. M. and Curran, J.M. (2016) Introduction to Bayesian Statistics 3rd Edition.   Wiley, New York 2.  Jim, A. (2009). Bayesian Computation with R, 2nd Edition, Springer. Essential Reading / Recommended Reading1. Berger, J.O. (1985a). Statistical Decision Theory and Bayesian Analysis, 2nd Ed. Springer-Verlag, New York. 2. Christensen R, Johnson, W., Branscum, A. and Hanson T. E. (2011). Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians, Chapman & Hall.  3. Congdon, P. (2006). Bayesian Statistical Modeling, Wiley  4. Ghosh, J. K., Delampady M. and T. Samantha (2006). An Introduction to Bayesian Analysis: Theory & Methods, Springer.  5. Rao. C.R. and Day. D. (2006). Bayesian Thinking, Modeling & Computation, Handbook of Statistics, Vol. 25. Elsevier. Evaluation PatternCIA 50% ESE 50% MST473B - CLINICAL TRIALS (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course is designed to train the students in the design and conduct of clinical trials and provide knowledge about the methods of statistical data analysis of clinical trials. Course Outcome CO1: Understand the study designs of randomized clinical trialsCO2: Apply statistical principles, concepts, and methods for the analysis of data in clinical trialsCO3: Demonstrate competencies in evaluating clinical research data and communicating resultsCO4: Demonstrate advanced critical thinking skills necessary to advance within the biopharmaceutical industry.
 Unit-1 Teaching Hours:15 Introduction to Clinical Trials Historical background of clinical trials - the need for clinical trials - ethics and planning of clinical trials - main features of study protocol - the selection of study subjects - treatment schedule - evaluation of patient response - follow-up studies - GCP/ICH guidelines                                                                                                                          Practical Assignments:       Exercise on designing case report forms. Exercise on the treatment schedule Unit-2 Teaching Hours:15 Phases of clinical trials Different phases of clinical trials: phase I, phase II, phase III, phase IV - Basic study designs -randomized controlled trials - non-randomized concurrent controlled trials - historical controls - cross over design - withdrawal design - hybrid designs - group allocation designs and studies of equivalency. Practical Assignments:       Exercise on various designs of clinical trials Exercise on the allocation of subjects to various groups Text Books And Reference Books: Friedman, L.M., Furberg, C.D., DeMets David L., (2015), Fundamentals of Clinical Trials 5th Edition, Springer. Meinert Curtis L., (2012), Clinical Trials-Design, conduct and Analysis, 2nd  Edition Oxford University Press, New York. Essential Reading / Recommended Reading Donald Campbell T., and Julian Stanley C., (1963), Experimental and Quasi Experimental designs for Research, Rand McNally and Company. Cochran William G., Gertrude Cox M., (1992) Experimetal Designs 2nd Edition, John Wiley and Sons. Chan A.W., Tetzlaff J.M., Altman D.G., Dickersin K., Moher D., (2013), New guidance for content of clinical trial protocol, Lancet 2013, Jan 12; 381(9861-91) Stuart Pocock J., (1996), Clinical Trials A practical approach, John Wiley and Sons. Evaluation PatternCIA - 50% ESE- 50% MST473C - RISK MODELING (2020 Batch) Total Teaching Hours for Semester:75 No of Lecture Hours/Week:5 Max Marks:150 Credits:4 Course Objectives/Course Description This course will equip students with a wide variety of statistical methods for modelling risk. Course Outcome CO1: Demonstrate the understanding of basic concepts of risk modelingCO2: Apply probabilistic concepts for modeling riskCO3: Analyze risk using statistical dose-response modelsCO4: Apply risk management to individual portfolio problems
 Unit-1 Teaching Hours:12 Basic Risk Models Distinguishing Characteristics Of Risk Analysis - Traditional Health Risk Analysis - Defining Risks: Source, Target, Effect, Mechanism - Basic Quantitative Risk Models - Risk as Probability of a Binary Event - Hazard Rate Models Practical Assignments: 1. Lab exercise on the quantitative risk model. 2.. Lab exercise on the hazard rate model Unit-2 Teaching Hours:18 Risk Assessment Modelling Conditional Probability Framework for Risk Calculations - Population Risks Modeled by Conditional Probabilities - Trees, Risks and Martingales - Compartmental Flow Simulation Models - Monte Carlo Uncertainty Analysis - Introduction to Exposure Assessment - Uncertainty Analysis Practical Assignments: 3.  Lab exercise on risk calculations. 4.  Lab exercise on risk modelling by conditional probabilities. 5. Lab exercise on  compartment flow simulation model. 6. Lab exercise on  Monte Carlo uncertainty analysis Text Books And Reference Books: Cox Jr, L. A. (2012). Risk analysis foundations, models, and methods. Springer Science & Business Media. Essential Reading / Recommended Reading   Pfaff, B. (2016). Financial risk modelling and portfolio optimization with R. John Wiley & Sons. Müller, A. C., & Guido, S. (2016). Introduction to machine learning with Python: a guide for data scientists. “O’Reilly Media, Inc." Gray, R. J., & Pitts, S. M. (2012). Risk modelling in general insurance: From principles to practice. Cambridge University Press. De Rocquigny, E. (2012). Modelling under risk and uncertainty: an introduction to statistical, phenomenological and computational methods. John Wiley & Sons. Evaluation PatternCIA - 50% ESE - 50% MST481 - SEMINAR PRESENTATION (2020 Batch) Total Teaching Hours for Semester:30 No of Lecture Hours/Week:2 Max Marks:50 Credits:1 Course Objectives/Course Description This course is to enhance the verbal and written presentation skills of students and to develop analytical skills as students learn new areas and ideas in Statistics. Course Outcome CO1: Demonstrate presentation and writing skills.
 Unit-1 Teaching Hours:30 Presentation 1. Prepare a report on a relevant topic. 2. Present it well before the class and panel members. Text Books And Reference Books:_ Essential Reading / Recommended Reading_ Evaluation PatternCIA 50% ESE 50%